What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
Submit your PRPs
See the Top discoverers
See the Latest PRPs
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 1251 | (71^172259-1)/70 | 318895 | Paul Bourdelais | 08/2020 |
| 1252 | 2^1058425+38507 | 318618 | Enzo Doria | 11/2024 |
| 1253 | -30*Bern(85996)/236037521 | 318354 | Sergey Batalov | 10/2023 |
| 1254 | (13^285707-1)/870834948 | 318253 | Paul Vanderveen | 05/2025 |
| 1255 | 2^1055665+30407 | 317787 | Enzo Doria | 03/2024 |
| 1256 | 2^1054736+483061 | 317508 | Enzo Doria | 12/2016 |
| 1257 | 2^1053965+1879667 | 317276 | Enzo Doria | 10/2016 |
| 1258 | (43^194119-1)/42 | 317086 | Paul Bourdelais | 08/2020 |
| 1259 | 2^1052899+225413 | 316955 | Enzo Doria | 08/2024 |
| 1260 | 2^1052186-458165 | 316740 | Enzo Doria | 03/2015 |
| 1261 | 11^303909+2 | 316489 | Paul Bourdelais | 08/2023 |
| 1262 | 2^1049026+214609 | 315789 | Enzo Doria | 11/2023 |
| 1263 | 2^1048576+69661 | 315653 | Boyan Hu | 08/2024 |
| 1264 | 2^1046613-114685 | 315062 | Enzo Doria | 04/2015 |
| 1265 | 2^1045625-459373 | 314765 | Enzo Doria | 06/2015 |
| 1266 | 10^(2*157363+1)-8*10^157363-1 | 314727 | Robert Price | 07/2023 |
| 1267 | (7*10^314564-61)/9 | 314564 | Erik Branger | 09/2016 |
| 1268 | 2^1044771+228023 | 314508 | Enzo Doria | 11/2024 |
| 1269 | 2^1044206+7 | 314338 | Stefano Morozzi | 10/2022 |
| 1270 | (7^371669-1)/6 | 314096 | Paul Bourdelais | 02/2010 |
| 1271 | (53^181981-1)/52 | 313784 | Paul Bourdelais | 08/2020 |
| 1272 | (8^347437-5^347437)/3 | 313767 | Jon Grantham | 08/2023 |
| 1273 | (10^313741+1)/11/11294677 | 313733 | Alfred Reich | 04/2024 |
| 1274 | 2^1041944+283051 | 313657 | Enzo Doria | 12/2016 |
| 1275 | (1624^97969-1)/(1624^313-1) | 313533 | Sergey Batalov | 11/2023 |
| 1276 | 2^1041153-114391 | 313419 | Enzo Doria | 02/2015 |
| 1277 | (2^1039700+9)/5 | 312981 | Stefano Morozzi | 09/2022 |
| 1278 | (74^167311+1)/75 | 312742 | Paul Bourdelais | 12/2020 |
| 1279 | 2^1038871+1866983 | 312732 | Enzo Doria | 04/2016 |
| 1280 | 2^1038545+71657 | 312634 | Enzo Doria | 08/2023 |
| 1281 | (55^179573-1)/54 | 312521 | Paul Bourdelais | 08/2020 |
| 1282 | 2^1037647+1881263 | 312363 | Enzo Doria | 11/2016 |
| 1283 | 2^1037226+1879699 | 312237 | Enzo Doria | 10/2016 |
| 1284 | 2^1036867+1865843 | 312129 | Enzo Doria | 02/2016 |
| 1285 | (76^165947+1)/77 | 312114 | Paul Bourdelais | 01/2021 |
| 1286 | 2^1036324+39091 | 311965 | Enzo Doria | 11/2024 |
| 1287 | 2^1036020-114539 | 311874 | Enzo Doria | 02/2015 |
| 1288 | (90^159463-1)/89 | 311628 | Paul Bourdelais | 08/2020 |
| 1289 | 2^1034546+28819 | 311430 | Enzo Doria | 02/2024 |
| 1290 | 2^1032240+1883431 | 310736 | Enzo Doria | 01/2017 |
| 1291 | 64211^64588+64588^64211 | 310514 | Norbert Schneider | 11/2023 |
| 1292 | 2^1031450+29629 | 310498 | Enzo Doria | 03/2024 |
| 1293 | 2^1030352+1870021 | 310167 | Enzo Doria | 06/2016 |
| 1294 | 2^1030046+1882843 | 310075 | Enzo Doria | 11/2016 |
| 1295 | 2^1029120+227971 | 309796 | Enzo Doria | 11/2024 |
| 1296 | 3^648872+16 | 309591 | Robert Price | 04/2020 |
| 1297 | (16976^73441-1)/(16976^271-1) | 309498 | Ryan Propper | 11/2023 |
| 1298 | 64221^64366+64366^64221 | 309451 | Norbert Schneider | 06/2023 |
| 1299 | (11121^76729-1)/(11121^277-1) | 309336 | Ryan Propper | 11/2023 |
| 1300 | 2^1027478+219259 | 309302 | Enzo Doria | 02/2024 |
| 1301 | 2^1026999+20513 | 309158 | Enzo Doria | 07/2023 |
| 1302 | 5^442281+2 | 309142 | Paul Bourdelais | 01/2021 |
| 1303 | 2^1026204+22741 | 308919 | Enzo Doria | 09/2023 |
| 1304 | 2^1026190+15 | 308914 | Stefano Morozzi | 10/2022 |
| 1305 | 2^1025108+20851 | 308589 | Enzo Doria | 08/2023 |
| 1306 | 2^1022860+234121 | 307912 | Enzo Doria | 03/2025 |
| 1307 | A352736(16) | 306985 | Kellen Shenton | 05/2022 |
| 1308 | 2^1019777+213947 | 306984 | Enzo Doria | 10/2023 |
| 1309 | 2^1018820+236731 | 306696 | Enzo Doria | 05/2025 |
| 1310 | (11^293831-1)/10 | 305993 | Paul Bourdelais | 03/2010 |
| 1311 | (67^167449-1)/66 | 305773 | Paul Bourdelais | 08/2020 |
| 1312 | (62^170539+1)/63 | 305671 | Paul Bourdelais | 12/2020 |
| 1313 | 2^1015321-1015321 | 305643 | Henri Lifchitz | 08/2013 |
| 1314 | 2^1014775+27113 | 305478 | Enzo Doria | 12/2023 |
| 1315 | 2^1014450+7 | 305380 | Stefano Morozzi | 10/2022 |
| 1316 | 2^1014404+46171 | 305367 | Enzo Doria | 05/2025 |
| 1317 | 2^1014336+215731 | 305346 | Enzo Doria | 12/2023 |
| 1318 | 2^1014224-2791229 | 305312 | Enzo Doria | 01/2016 |
| 1319 | (10^304986+7)/673 | 304984 | Alfred Reich | 11/2021 |
| 1320 | 65473^45250+45250^65473 | 304818 | Hans Havermann | 02/2022 |
| 1321 | 66012^41423+41423^66012 | 304794 | Hans Havermann | 03/2022 |
| 1322 | 65073^48202+48202^65073 | 304742 | Hans Havermann | 04/2022 |
| 1323 | 2^1012054+31669 | 304659 | Enzo Doria | 06/2024 |
| 1324 | 238176^19+19^238176 | 304569 | Hans Havermann | 03/2022 |
| 1325 | 73122^14615+14615^73122 | 304539 | Hans Havermann | 05/2022 |
| 1326 | 64492^52639+52639^64492 | 304487 | Hans Havermann | 03/2022 |
| 1327 | 65955^41288+41288^65955 | 304437 | Hans Havermann | 04/2022 |
| 1328 | 71729^17530+17530^71729 | 304403 | Hans Havermann | 03/2022 |
| 1329 | 70170^21733+21733^70170 | 304336 | Hans Havermann | 03/2022 |
| 1330 | 2^1010751-107709 | 304267 | Enzo Doria | 03/2014 |
| 1331 | 84473^3994+3994^84473 | 304222 | Hans Havermann | 03/2022 |
| 1332 | (2^1010623-1)/12602017578957977 | 304212 | Tony Prest / Never Odd Or Even | 02/2014 |
| 1333 | 74442^12125+12125^74442 | 303998 | Hans Havermann | 02/2022 |
| 1334 | 77842^8039+8039^77842 | 303989 | Hans Havermann | 01/2022 |
| 1335 | 64209^54140+54140^64209 | 303935 | Hans Havermann | 02/2022 |
| 1336 | 2^1009577+1869587 | 303913 | Enzo Doria | 06/2016 |
| 1337 | 67389^32338+32338^67389 | 303906 | Hans Havermann | 02/2022 |
| 1338 | 8^336419-7^336419 | 303817 | Jean-Louis Charton | 01/2008 |
| 1339 | 2^1009168+15 | 303790 | Stefano Morozzi | 10/2022 |
| 1340 | 80766^5771+5771^80766 | 303782 | Hans Havermann | 01/2022 |
| 1341 | 66094^39385+39385^66094 | 303724 | Hans Havermann | 01/2022 |
| 1342 | 69147^24574+24574^69147 | 303589 | Hans Havermann | 02/2022 |
| 1343 | 78390^7459+7459^78390 | 303580 | Hans Havermann | 01/2022 |
| 1344 | 2^1008301+1869377 | 303529 | Enzo Doria | 06/2016 |
| 1345 | 65008^46615+46615^65008 | 303492 | Hans Havermann | 02/2022 |
| 1346 | (2^1007838+5)/3 | 303389 | Serge Batalov | 08/2015 |
| 1347 | 65018^46293+46293^65018 | 303343 | Hans Havermann | 01/2022 |
| 1348 | 6^389756+5 | 303290 | Paul Bourdelais | 02/2021 |
| 1349 | 71016^18649+18649^71016 | 303285 | Hans Havermann | 01/2022 |
| 1350 | 2^1007065+29231 | 303157 | Enzo Doria | 03/2024 |
| 1351 | 80160^6047+6047^80160 | 303129 | Hans Havermann | 01/2022 |
| 1352 | 67434^31237+31237^67434 | 303094 | Hans Havermann | 03/2022 |
| 1353 | 65537^42102+42102^65537 | 303063 | Hans Havermann | 02/2022 |
| 1354 | 71790^16553+16553^71790 | 302874 | Hans Havermann | 11/2021 |
| 1355 | 65208^44129+44129^65208 | 302874 | Hans Havermann | 11/2021 |
| 1356 | 84181^3960+3960^84181 | 302858 | Hans Havermann | 11/2021 |
| 1357 | (13703^73441-1)/(13703^271-1) | 302691 | Ryan Propper | 11/2023 |
| 1358 | 71956^16087+16087^71956 | 302682 | Hans Havermann | 11/2021 |
| 1359 | 2^1005326+383059 | 302634 | Enzo Doria | 12/2016 |
| 1360 | 2^1004929+1877567 | 302514 | Enzo Doria | 08/2016 |
| 1361 | 69341^22978+22978^69341 | 302418 | Hans Havermann | 12/2021 |
| 1362 | 111443^516+516^111443 | 302306 | Hans Havermann | 12/2021 |
| 1363 | 67638^29387+29387^67638 | 302218 | Hans Havermann | 11/2021 |
| 1364 | 2^1003494+1874899 | 302082 | Enzo Doria | 06/2016 |
| 1365 | 75189^10400+10400^75189 | 302037 | Hans Havermann | 12/2021 |
| 1366 | 67237^31042+31042^67237 | 302026 | Hans Havermann | 12/2021 |
| 1367 | 64540^47791+47791^64540 | 302005 | Hans Havermann | 11/2021 |
| 1368 | 2^1003046+60529 | 301947 | Enzo Doria | 04/2016 |
| 1369 | 83278^4209+4209^83278 | 301815 | Hans Havermann | 09/2021 |
| 1370 | 64431^48250+48250^64431 | 301763 | Hans Havermann | 09/2021 |
| 1371 | 67237^30714+30714^67237 | 301716 | Hans Havermann | 09/2021 |
| 1372 | 2^1002144+235861 | 301676 | Enzo Doria | 05/2025 |
| 1373 | 64641^46288+46288^64641 | 301581 | Hans Havermann | 09/2021 |
| 1374 | 71513^16482+16482^71513 | 301572 | Hans Havermann | 10/2021 |
| 1375 | 72017^15396+15396^72017 | 301565 | Hans Havermann | 09/2021 |
| 1376 | 65534^39927+39927^65534 | 301540 | Hans Havermann | 10/2021 |
| 1377 | (23^221411-1)/22 | 301501 | Paul Bourdelais | 08/2020 |
| 1378 | 63169^59152+59152^63169 | 301441 | Hans Havermann | 09/2021 |
| 1379 | 75055^10348+10348^75055 | 301336 | Hans Havermann | 09/2021 |
| 1380 | 2^1000647+1881353 | 301225 | Enzo Doria | 11/2016 |
| 1381 | 83686^3961+3961^83686 | 301086 | Hans Havermann | 10/2021 |
| 1382 | 68529^24742+24742^68529 | 301078 | Hans Havermann | 09/2021 |
| 1383 | 65207^41416+41416^65207 | 301072 | Hans Havermann | 10/2021 |
| 1385 | 2^1000000+821751 | 301030 | Tony Prest / Never Odd Or Even | 10/2015 |
| 1384 | 2^999999+77151 | 301030 | Norman Luhn | 09/2023 |
| 1386 | 90762^2071+2071^90762 | 300984 | Hans Havermann | 06/2021 |
| 1387 | 63909^51142+51142^63909 | 300934 | Hans Havermann | 08/2021 |
| 1388 | 2^999646+1874029 | 300924 | Enzo Doria | 06/2016 |
| 1389 | 66280^34607+34607^66280 | 300856 | Hans Havermann | 06/2021 |
| 1390 | 65534^38925+38925^65534 | 300817 | Hans Havermann | 07/2021 |
| 1391 | 63296^56517+56517^63296 | 300794 | Hans Havermann | 06/2021 |
| 1392 | 110610^523+523^110610 | 300694 | Hans Havermann | 06/2021 |
| 1393 | 66428^33609+33609^66428 | 300684 | Hans Havermann | 06/2021 |
| 1394 | 74247^11210+11210^74247 | 300672 | Hans Havermann | 06/2021 |
| 1395 | (59^169777-1)/58 | 300649 | Paul Bourdelais | 08/2020 |
| 1396 | 10^300476+3 | 300477 | Ed Trice | 10/2012 |
| 1397 | 10^300476-530913 | 300476 | Patrick De Geest | 03/2016 |
| 1398 | 66703^31960+31960^66703 | 300471 | Hans Havermann | 06/2021 |
| 1399 | 63722^51915+51915^63722 | 300468 | Hans Havermann | 06/2021 |
| 1400 | 2^998053+1879667 | 300444 | Enzo Doria | 09/2016 |
| 1401 | 77018^7959+7959^77018 | 300437 | Hans Havermann | 07/2021 |
| 1402 | 314738^9+9^314738 | 300337 | Anatoly F. Selevich | 02/2011 |
| 1403 | 2^997689+217787 | 300335 | Enzo Doria | 01/2024 |
| 1404 | 69478^20987+20987^69478 | 300281 | Hans Havermann | 07/2021 |
| 1405 | 64088^48393+48393^64088 | 300239 | Hans Havermann | 07/2021 |
| 1406 | 2^997369+237917 | 300238 | Enzo Doria | 06/2025 |
| 1407 | 64605^44146+44146^64605 | 300084 | Hans Havermann | 08/2021 |
| 1408 | 2^996845+29027 | 300081 | Enzo Doria | 02/2024 |
| 1409 | 7^355039-6^355039 | 300043 | Jean-Louis Charton | 05/2011 |
| 1410 | 67594^27465+27465^67594 | 300035 | Hans Havermann | 06/2021 |
| 1411 | 10^300000+287389 | 300001 | Patrick De Geest | 10/2019 |
| 1412 | 10^300000-83657 | 300000 | Patrick De Geest | 10/2019 |
| 1413 | 70599^17756+17756^70599 | 300000 | Hans Havermann | 06/2021 |
| 1414 | numbpart(72526161452) | 299999 | Serge Batalov | 04/2017 |
| 1415 | 2^996182-114431 | 299881 | Enzo Doria | 02/2015 |
| 1416 | 3*2^996126+5 | 299865 | Jon Grantham | 07/2023 |
| 1417 | 2^996034-17 | 299837 | Stefano Morozzi | 07/2022 |
| 1418 | 2^995793+36587 | 299764 | Enzo Doria | 09/2024 |
| 1419 | (19*10^299640+77)/3 | 299641 | Robert Price | 03/2023 |
| 1420 | 2^995214-2788361 | 299590 | Enzo Doria | 12/2015 |
| 1421 | 2^994791-114319 | 299462 | Enzo Doria | 01/2015 |
| 1422 | 2^994490-1863791 | 299372 | Enzo Doria | 01/2016 |
| 1423 | 2^993322+1885729 | 299020 | Enzo Doria | 03/2017 |
| 1424 | 2^993227+230033 | 298992 | Enzo Doria | 12/2024 |
| 1425 | (36395^65536+36393^65536)/2 | 298913 | Kellen Shenton | 04/2022 |
| 1426 | 2^992711-2788807 | 298836 | Enzo Doria | 12/2015 |
| 1427 | 2^992525-114199 | 298780 | Enzo Doria | 12/2014 |
| 1428 | (7^353501-3^353501)/4 | 298743 | Jon Grantham | 08/2023 |
| 1429 | 2^992329+1884707 | 298721 | Enzo Doria | 02/2017 |
| 1430 | 2^992292+229801 | 298710 | Enzo Doria | 12/2024 |
| 1431 | 2^992052+215491 | 298638 | Enzo Doria | 11/2023 |
| 1432 | 2^991968-23 | 298613 | Stefano Morozzi | 07/2022 |
| 1433 | 2^991715-19 | 298536 | Stefano Morozzi | 07/2022 |
| 1434 | 2^991387+237383 | 298438 | Enzo Doria | 06/2025 |
| 1435 | (10^298414+7)/191/823/56921/1334467 | 298398 | Alfred Reich | 10/2021 |
| 1436 | 2^989562+25 | 297888 | Stefano Morozzi | 05/2021 |
| 1437 | 2^988580+214051 | 297593 | Enzo Doria | 10/2023 |
| 1438 | 2^988537+218837 | 297580 | Enzo Doria | 03/2024 |
| 1439 | (19*10^297497+77)/3 | 297498 | Robert Price | 03/2023 |
| 1440 | (2*10^297488-23)/3 | 297488 | Robert Price | 10/2022 |
| 1441 | 2^988148+48271 | 297463 | Enzo Doria | 07/2025 |
| 1442 | 2^987033+46427 | 297127 | Enzo Doria | 05/2025 |
| 1443 | (2^986191+1)/3 | 296873 | Vincent Diepeveen | 06/2008 |
| 1444 | 2^985217-114553 | 296580 | Enzo Doria | 03/2015 |
| 1445 | (76^157649-1)/75 | 296507 | Paul Bourdelais | 07/2019 |
| 1446 | 2^984650+21529 | 296410 | Enzo Doria | 08/2023 |
| 1447 | 2^984131-1828009 | 296253 | Enzo Doria | 01/2015 |
| 1448 | 2^983620+60451 | 296100 | Phil Moore | 03/2008 |
| 1449 | 2^982721-2683 | 295829 | Yves Minet | 02/2016 |
| 1450 | (23*10^295581+7)/3 | 295582 | Robert Price | 05/2023 |
| 1451 | 2^981298-2788421 | 295401 | Enzo Doria | 12/2015 |
| 1452 | 2^981163-2790967 | 295360 | Enzo Doria | 12/2015 |
| 1453 | 2^981016-15 | 295316 | Stefano Morozzi | 07/2022 |
| 1454 | 8*10^295160-13 | 295161 | Robert Price | 08/2023 |
| 1455 | 2^979594+1865839 | 294888 | Enzo Doria | 02/2016 |
| 1456 | 2^979502+221029 | 294860 | Enzo Doria | 03/2024 |
| 1457 | 2*10^294527-91 | 294528 | Robert Price | 02/2023 |
| 1458 | (49363^63001-1)/(49363^251-1) | 294511 | Ryan Propper | 11/2023 |
| 1459 | 10^294475+49 | 294476 | Robert Price | 02/2023 |
| 1460 | 2^977896+234601 | 294377 | Enzo Doria | 04/2025 |
| 1461 | (11*10^294308+91)/3 | 294309 | Robert Price | 03/2023 |
| 1462 | 2^976760+1885021 | 294035 | Enzo Doria | 02/2017 |
| 1463 | 3*2^976518+5 | 293962 | Jon Grantham | 07/2023 |
| 1464 | 2^975798+218599 | 293745 | Enzo Doria | 01/2024 |
| 1465 | 2^974441+1878407 | 293336 | Enzo Doria | 08/2016 |
| 1466 | 2^974180+1876831 | 293258 | Enzo Doria | 07/2016 |
| 1467 | 2^974170+453319 | 293255 | Enzo Doria | 01/2017 |
| 1468 | (211^126023-1)/210 | 292911 | Anonymous | 05/2024 |
| 1469 | 2^972744-114419 | 292826 | Enzo Doria | 03/2015 |
| 1470 | 11^281143+6 | 292781 | Paul Bourdelais | 03/2021 |
| 1471 | (4*10^292619-91)/3 | 292620 | Robert Price | 12/2022 |
| 1472 | E(69468)/13247122135 | 292549 | Sergey Batalov | 10/2023 |
| 1473 | CopelandErdos(292447) | 292447 | Mark Rodenkirch | 12/2015 |
| 1474 | 3*10^292344-97 | 292345 | Robert Price | 01/2023 |
| 1475 | 2^970911+1873373 | 292274 | Enzo Doria | 07/2016 |
| 1476 | 2^970670+383059 | 292201 | Enzo Doria | 12/2016 |
| 1477 | 2^970141-100363 | 292042 | Enzo Doria | 02/2014 |
| 1478 | 2^969945+1874717 | 291983 | Enzo Doria | 06/2016 |
| 1479 | 2^969384+1880701 | 291814 | Enzo Doria | 10/2016 |
| 1480 | (13*10^291721-43)/3 | 291722 | Robert Price | 08/2023 |
| 1481 | (3^611333-2^611333)/(99035947*87109884549431) | 291659 | Mike Oakes | 02/2017 |
| 1482 | 10^(2*145126+1)-2*10^145126-1 | 290253 | Robert Price | 03/2025 |
| 1483 | 3*2^963892+5 | 290161 | Jon Grantham | 07/2023 |
| 1484 | (151*10^289877-1)/3 | 289879 | Robert Price | 07/2023 |
| 1485 | 2^962194+60139 | 289650 | Enzo Doria | 02/2016 |
| 1486 | 2^961409+44267 | 289413 | Enzo Doria | 04/2025 |
| 1487 | 2^959307-1861507 | 288781 | Enzo Doria | 11/2015 |
| 1488 | (17*10^288692+31)/3 | 288693 | Robert Price | 04/2023 |
| 1489 | 14^251797-3 | 288592 | Paul Bourdelais | 12/2020 |
| 1490 | (8745^73441-1)/(8745^271-1) | 288419 | Ryan Propper | 11/2023 |
| 1491 | (2*10^288371-23)/3 | 288371 | Robert Price | 10/2022 |
| 1492 | (31*10^288238-1)/3 | 288240 | Robert Price | 02/2023 |
| 1493 | (7^341063-2^341063)/5 | 288231 | Jon Grantham | 08/2023 |
| 1494 | 2^957372+283531 | 288198 | Enzo Doria | 02/2017 |
| 1495 | 2^957192-1864049 | 288144 | Enzo Doria | 01/2016 |
| 1496 | (95774^58081-1)/(95774^241-1) | 288116 | Ryan Propper | 11/2023 |
| 1497 | 2^956446+1875199 | 287919 | Enzo Doria | 06/2016 |
| 1498 | 2^956283+219143 | 287870 | Enzo Doria | 02/2024 |
| 1499 | 7*10^287854+39 | 287855 | Robert Price | 01/2023 |
| 1500 | 2^956082+28309 | 287810 | Enzo Doria | 02/2024 |
